Question 1: The group of all high school graduates is very diverse and differs greatly from the group of the college bound graduates. All will be the voting citizenry of our future. A quality mathematics education is a vital component in producing the next generation of leaders and citizens who understand our complex world. I mention this because many and maybe most high schools have a two year graduation requirement for mathematics. These courses do not necessarily include any college preparatory mathematics and are often completed in the 9th and 10th grade years, leaving students void of any mathematical study thereafter. Many of these graduates become the growing population of people trying to reenter college or training programs after they have discovered the ``hard way'' that they are not qualified for the job market. I am greatly concerned about this large population of high school graduates, not to mention my concern for the growing number of drop-outs, and I strongly feel that the mathematics courses offered in high school are the ``gatekeepers'' for all of these students. For many students, their first mathematics course in high school is another arithmetic review course or an algebra course based on memorizing procedures. Bored and not seeing any relevance, these students often quit their study of mathematics after the minimum requirement is met. To keep more students studying more mathematics, we---the entire mathematics education community---should take a long and hard look at our long standing practices of what high school mathematics is and how it is taught.

With this in mind, I'll respond to the question. I want my students to be confident problem solvers---that is they can solve complex problems that they have not seen before. Students should be able to use many strategies and approaches to start the problem solving process---not just mimic some procedure they have memorized. Students should have a deep understanding of the concepts used in algebra, geometry, probability, statistics, and discrete mathematics and should understand the connections between these branches of mathematics. I want students to know when it is appropriate to use technology and how to use it to further investigations and discovery. I want all students to be competent doing mental mathematics when needed and able to estimate when necessary.

Question 2: The structure of the curriculum must change. Let's give up this centuries old notion that one must master mathematics in a given order (arithmetic, algebra, geometry, trigonometry...) and let's look at teaching all students all the branches of mathematics every year they are in school. The curriculum must be based on solving complex problems and putting the skills that need to be learned in context. Every student needs to study probability and statistics - topics that have been largely omitted in the past.

Question 3: We never will unless we agree on what is important and how we should hold the system accountable. If I teach my students problem solving skills, topics other than algebra and geometry, and I require the use of graphing calculators, and then these students take placement tests at college that are based on the "old" curriculum, then we will never know if the programs are working. We could show increased numbers of students taking more high school mathematics courses, but there is always going to be a cry that we have only lowered the standards. We, again the entire mathematics education community, need to agree on what is important to teach and how we are going to measure student performance.

Question 4: High school mathematics teachers should have a degree in mathematics or mathematics education. They should have a love and appreciation for their subject area. I feel strongly that they should have an interest in joining professional mathematics organizations, read journals, and attend conferences to stay informed about their subject area. Good mathematics teachers should be interested in discussing best teaching practices with colleagues and be involved in the curriculum development in their school. Teachers should be interested in continuing to improve their teaching by looking for new methods and strategies and not assume that teaching the way you were taught is the best method.

Question 5: Several outstanding mathematics teachers in my junior high school and high school years got me excited about the subject. Although I "failed" the 8th grade placement test for entering high school algebra (important tests made me very nervous), a very caring teacher had confidence in me and allowed me to enter the course. From that time on, my interest in mathematics grew. I often wonder how many interested and talented students there are who have not had someone to care about them as I did and therefore their opportunities ended.

Question 6: My expectations for higher education are similar to my own goals for students. I want them to have opportunities to continue to develop their problem solving abilities. I want students to learn the necessary skills in each course they take, but I want those skills to be taught in some context. I hope all students continue to put the pieces of the mathematics puzzle together, making connections between all areas of mathematics. Students should use the technologies available in all of their courses. Most importantly I hope that calculus won't be the filter in higher education as algebra has been in high school. Hopefully prospective mathematics teachers will have seen many models of good teaching throughout their college/university courses. We tend to teach as we were taught, so seeing a variety of styles, techniques, and strategies is very important.